Technical Field
The present invention relates to fiber optic sensors. Particular embodiments relate to sensors with nested optical cavities utilizing Fabry-Perot interferometry.
Discussion of Art
Fiber optic sensors with nested optical cavities, using Fabry-Perot interferometry, can simultaneously sense multiple measurands and have broadly-recognized industrial applicability.
Nested optical cavities have at least two concatenated cavities 1, 2 that are formed by three or more optical interfaces 3, 4, 5 as shown in FIG. 1. Generally, each two adjacent mediums (FIG. 1) have a different refractive index. Therefore, a portion of incoming light will be reflected back from an interface between two adjacent mediums. For example, an interface 3 at the “front” (input) side of cavity 1 reflects a portion of incoming light as E1. Similarly, E2 and E3 are reflected, respectively, from interfaces 4 and 5 between cavity 1 and cavity 2 and at the rear wall of cavity 2.
If an optical path difference (OPD) between any two of the reflected beams E1, E2, or E3 is within a coherence length of the light source that provides Ein, then the two beams will generate interference fringes. Typically the OPD values of three different combinations are smaller than the light source coherence length.
Therefore, the multiple optical interfaces 3, 4, 5 will together produce a composite interference signal whose characteristics depend upon the dimensions and refractive indices of the individual cavities 1, 2. FIG. 2, which is a broadband amplitude/wavelength spectrum graph, shows a composite interference signal encoded by the nested optical cavities 1, 2 into the light reflected therefrom.
Several signal demodulation techniques are known for interferometry of a single cavity. For example, Fourier transform method has advantages of fast computation and absolute measurement, but offers low resolution of cavity dimensions. Cross correlation method has drawbacks of either a time-consuming computation, or the requirement of an external analyzing interferometer. Additionally, cross correlation presents a 2 pi phase ambiguity problem, i.e., cavity dimension may be more precise than Fourier but significantly inaccurate. Least-square fitting method has the same limitations as cross correlation, i.e., time-consuming computation and 2 pi phase ambiguity problem. Wavelength tracking method offers high resolution but provides only a relative thickness measurement (i.e., which cavity is thicker?) and small dynamic range (half-wavelength limitation). A modified wavelength tracking method tracks the fringe peak or valley wavelength and the corresponding fringe order by using two fringe peaks or valleys. The modified wavelength tracking method provides absolute measurement for only one cavity demodulation with high resolution but may induce 2 pi phase ambiguity due to noise effect on either of the two fringe peaks or valleys.
Unfortunately there is a dearth of effective and efficient demodulation methods to calculate the thicknesses of nested cavities and the physical measurands. Currently cross-correlation is known to work as a demodulation method for nested cavities when used with an external analyzing interferometer or using time intensive computational software. However, when the difference of the thicknesses of the cavities is small, the problem is severe and the algorithm almost cannot resolve the accurate thicknesses. Computational load can be such as to prohibit cost-effective “real-time” measurement (i.e., measurement that produces a signal indicative of a measurand, during a period of time that the measurand holds a near-constant value).
Accordingly, it is desirable to have an accurate, timely and cost effective method for demodulating optical signals produced by nested cavities.